Add boiling water to split peas in a large pot and boil for 2 minutes.
Remove from heat, cover tightly, and let soak for 1 hour.
Add ham bone, chopped onions, diced carrot, sliced potato, salt, and pepper to the pot.
Cook slowly over medium-low heat until peas are tender, approximately 45 minutes.
Remove ham bone from the soup.
For smooth soup, rub peas through a sieve, or leave unstrained for rustic texture.
Season with additional salt and pepper to taste.
If soup is too thick, add water to reach desired consistency.
Garnish with diced ham before serving.